(NEED ASAP!) Algebra I Word Problem

Question

You are given the task of opening a snow cone stand at your local high school football game. You are given $100 to buy needed supplies for the stand. You still need to purchase the ice blocks for $3.00 a block and the paper cones that cost $4.00 for a box of 30.  

1) Write an equation that represents different ways you could buy the ice blocks and paper cones.

2) How would you draw a graph that represents the equation you wrote?

3) Is this a linear function? If so, how do you know?

4) If a parent donated several boxes of paper cones so you no longer needed to buy any, how many blocks of ice could you buy?

Answer 1

Hello, Olivia,

Total funds are $100, We can spend that amount by purchasing ice blocks and paper cones. Let's set the following terms:

X = number of ice blocks at $3 each block

Y = number of boxes of cones at $4 per box (30 cones)

The equation can be written as the total funds is equal to the number of ice blocks x $3/block, plus the number of cone boxes x $4/box.

100 = 3X + 4Y

If we know the ratio required of cones per ice cube, we could solve this for exact counts of each to reach $100. Since we don't, there can be any number of combinations that would add up to, or less than, $100. Rearrange the equation to a more familiar format of Y = . . . . .:

Y = -0.75X + 25

We can tell immediately this is a straight line, with negative slope of -0.75, and an intercept of 25. A graph would show that if we purchase no ice blocks (X=0), we can buy up to 25 boxes of cones (Y=25) for a total expense of $100. All values under the line are valid, but remember that negative values for X and Y represent selling back (reducing the number), so aren't valid numbers. Valid numbers are the section of the line between where it crosses the X and Y. axes.

For part 4, the number of donated cones simply reduces the value of Y entered in the equation.

I hope this helps, Bob.

Answer 2

1. 3x + 4y = 100, where x=number of ice blocks you buy and y=boxes of 30 cones.
2. Can rewrite y as function of x, 4y=100-3x, and dividing both sides by 4, y= -3x/4 + 25. Using the form y=mx+b, the y-intercept is 25, and the slope is -3/4 (down 3, to the right 4). The graph can be plotted using these two points.
3. Yes. The function is a straight line (since it fits y=mx+b).
4. Remove "y" from the equation from part 1. Left with 3x=100, or x=33.3333.... Since you cannot buy a fraction of an ice block, you can buy 33 ice blocks.